Devices for a motor-driven adjustment of a vehicle door are already well-known. Typically, an electric motor is used to power an adjustment mechanism of a device to open and close are hinged vehicle door relative to a body structure of the vehicle so that a user may displace the vehicle door without pulling or pushing it. So far, different devices for a motor-driven adjustment of a vehicle door have been proposed. Such devices are usually rather complex and nee lots of space in an interior of the vehicle door and/or at the body structure of the vehicle. Addressing these difficulties WO 2017/029062 A1, for example, proposes to use an adjustment mechanism including a traction mechanism with a flexible traction member in the form of a rope for providing a device by means of which a vehicle door may be adjusted both manually and by means of a motor drive unit of the device. In this device the rope is connected with both ends to an elongated check arm of the device. An adjustment force may be applied by cable drum to which a part of the rope is wound. There is a need for a differently designed device for a motor-driven adjustment of vehicle door, in particular for a device with a smaller package size.